A bio-inspired geometric model for sound reconstruction

The reconstruction mechanisms built by the human auditory system during sound reconstruction are still a matter of debate. The purpose of this study is to propose a mathematical model of sound reconstruction based on the functional architecture of the auditory cortex (A1). The model is inspired by t...

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Bibliographic Details
Published in:Journal of mathematical neuroscience 2021-01, Vol.11 (1), p.2-2, Article 2
Main Authors: Boscain, Ugo, Prandi, Dario, Sacchelli, Ludovic, Turco, Giuseppina
Format: Article
Language:English
Subjects:
Acoustics
Algorithms
Analysis of PDEs
Applications of Mathematics
Biomimetics
Cognitive science
Differential equations
Engineering Sciences
Fourier transforms
Image reconstruction
Linguistics
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Mathematics and Statistics
Neurosciences
Optimization and Control
Signal and Image processing
Sound
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Summary:The reconstruction mechanisms built by the human auditory system during sound reconstruction are still a matter of debate. The purpose of this study is to propose a mathematical model of sound reconstruction based on the functional architecture of the auditory cortex (A1). The model is inspired by the geometrical modelling of vision, which has undergone a great development in the last ten years. There are, however, fundamental dissimilarities, due to the different role played by time and the different group of symmetries. The algorithm transforms the degraded sound in an ‘image’ in the time–frequency domain via a short-time Fourier transform. Such an image is then lifted to the Heisenberg group and is reconstructed via a Wilson–Cowan integro-differential equation. Preliminary numerical experiments are provided, showing the good reconstruction properties of the algorithm on synthetic sounds concentrated around two frequencies.
ISSN:2190-8567
2190-8567
DOI:10.1186/s13408-020-00099-4